At ICO, you can only use a TI-30 series. That means you could use a TI-34 or whatever, as long as it is a 3x. That is also the rule for the NBEO.
As far as why you can use a calculator on the NBEO, and not on any of the admission test is very clear. At least for the MCAT and OAT, the math is relativly basic algebra. Most of the reason for those exams is to see how you think on your feet. On the NBEo, you will be doing Optics, and they want to see if you can get the answer. They tested your math abilities on the OAt, now they just want to make sure you can apply what you learned.